Multiply the following complex numbers: $({-5-4i}) \cdot ({4})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5-4i}) \cdot ({4}) = $ $ ({-5} \cdot {4}) + ({-5} \cdot {0}i) + ({-4}i \cdot {4}) + ({-4}i \cdot {0}i) $ Then simplify the terms: $ (-20) + (0i) + (-16i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (0 - 16)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (0 - 16)i - 0 $ The result is simplified: $ (-20 - 0) + (-16i) = -20-16i $